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Construction of dense maximal-dimensional hypercyclic subspaces for Rolewicz operators

Author

Listed:
  • Bernal-González, L.
  • Calderón-Moreno, M.C.
  • Fernández-Sánchez, J.
  • Muñoz-Fernández, G.A.
  • Seoane-Sepúlveda, J.B.

Abstract

In this paper, weighted backward shift operators Tw associated to a Schauder basis of a Banach space are considered. These operators are emblematic in the setting of linear chaos in topological vector spaces. In a constructive way, it is shown the existence of a dense linear subspace having maximal dimension, all of whose nonzero members are simultaneously Tw-hypercyclic for every w belonging to a sequence of admissible weights. Our proof does not use any general result about algebraic or topological genericity.

Suggested Citation

  • Bernal-González, L. & Calderón-Moreno, M.C. & Fernández-Sánchez, J. & Muñoz-Fernández, G.A. & Seoane-Sepúlveda, J.B., 2022. "Construction of dense maximal-dimensional hypercyclic subspaces for Rolewicz operators," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    • Handle: RePEc:eee:chsofr:v:162:y:2022:i:c:s096007792200618x
    DOI: 10.1016/j.chaos.2022.112408
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